Calculate $\backslash$Delta G $($in kJ$/$mol$)$ for the reaction ADP $+$ Pi $+$ H$+$ ATP $+$ H$2$O using the proton motive force $(\backslash$Delta pH and $\backslash$Delta $\backslash$Psi $)$ generated during oxidative phosphorylation. $(10$ points$)$ Consider that:

ADP and Pi concentration $=10\backslash$mu M

ATP concentration $=5$ mM

pH gradient $(\backslash$Delta pH$)=1\mathrm{.}0($pH difference between mitochondrial matrix and intermembrane space$)$

Membrane potential $(\backslash$Delta $\backslash$Psi $)=-180$ mV $($inside negative with respect to outside$)$

$\backslash$Delta G$\text{'}$ for ATP synthesis at pH $7$ and $25\backslash$deg C$,$ which is $-30\mathrm{.}5$ kJ$/$mol

Gas constant $(8\mathrm{.}314$ J$/($mol$$K$))$

F is the Faraday constant $(96\mathrm{.}485$ kC$/$mol$).$

T in Kelvin $(298$ K$)$

$1$ proton is translocated during the synthesis of one ATP molecule.